Some years later of the original solution, a Gödel-type metric has been developed [1]}. This metric provides more information about the existence of CTCs. From this solution, a critical radius \(r_c\) , beyond which the causality is violated, can be constructed. The causality problem has been analyzed in various modified theories of gravity [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. Considering different contents of matter, such as the perfect fluid and the scalar field, the question of breakdown of causality in Palatini \(f(R, T)\)  gravity theory is examined.
